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arxiv: 2604.21857 · v2 · submitted 2026-04-23 · ✦ hep-ph · hep-ex· quant-ph

Recognition: unknown

Odd Physics Off the Diagonal: Constraining CP-violating SMEFT with Quantum Tomography

Avalon Roberts , Patrick Dougan , Alexander Oh , Savanna Shaw
Authors on Pith no claims yet

Pith reviewed 2026-05-09 21:33 UTC · model grok-4.3

classification ✦ hep-ph hep-exquant-ph
keywords SMEFTCP violationquantum tomographydiboson productionspin density matrixnew physicselectroweak operatorsangular observables
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The pith

Reconstructing the full spin density matrix of diboson systems reveals both linear and quadratic CP-violating SMEFT effects that standard angular observables overlook.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that new sources of CP violation needed to explain the matter-antimatter asymmetry can be introduced through SMEFT operators, but these signatures are often hidden or degenerate with CP-even effects in ordinary measurements. By applying quantum tomography to rebuild the complete spin density matrix of pairs of bosons produced at colliders, the method captures the entire pattern of new physics, including the pure quadratic terms that appear only at higher order. This provides simultaneous sensitivity to the characteristic features of both CP-even and CP-odd contributions in a way that goes beyond the limited information from azimuthal angles alone.

Core claim

Reconstructing the spin density matrix of a diboson system via quantum tomography extracts the full signature of beyond-Standard-Model physics, including the quadratic new-physics terms, and yields superior simultaneous sensitivity to CP-even and CP-odd SMEFT operators compared with traditional angular observables that rely primarily on interference resurrection.

What carries the argument

The spin density matrix of the diboson system, reconstructed through quantum tomography, which encodes the complete set of polarisation and correlation information including both SM-NP interference and pure quadratic NP contributions.

If this is right

  • CP-violating SMEFT operators become distinguishable from CP-even ones even when interference is suppressed.
  • Quadratic new-physics terms in diboson production can be directly constrained without relying solely on angular asymmetries.
  • Traditional polarisation-blind observables miss part of the new-physics signature that the full density matrix captures.
  • The same tomography method can be applied to other vector-boson final states to test additional SMEFT operators.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the method works at the LHC or a future collider, it could tighten global SMEFT fits by adding independent handles on CP phases.
  • The approach might extend to other correlated particle systems where full quantum-state reconstruction is feasible.
  • Improved detector resolution on decay angles would directly translate into better limits on the size of quadratic CP-odd operators.

Load-bearing premise

That collider detectors can reconstruct the diboson spin density matrix at high enough precision for the quadratic new-physics terms to be extracted without being swamped by systematic uncertainties or acceptance effects.

What would settle it

A measurement in which the reconstructed diboson spin density matrix elements remain too uncertain to separate the quadratic CP-odd SMEFT contributions from CP-even ones at the level predicted by the tomography approach.

Figures

Figures reproduced from arXiv: 2604.21857 by Alexander Oh, Avalon Roberts, Patrick Dougan, Savanna Shaw.

Figure 1
Figure 1. Figure 1: The ϕtruth distribution at LO for the pro￾cess pp → W+Z → e +νeµ +µ − with the inclusive setup of Ref. [27], applying the invariant mass cut 81 GeV < Mµ+µ− < 101 GeV. The upper panel shows the differential cross section dσ/dϕ∗ e in units of fb, comparing the SM prediction (red) with the SM + interference and SM + interference + quadratic contri￾butions for ceven = 1.0 (solid) and codd = 1.0 (dashed). The m… view at source ↗
Figure 2
Figure 2. Figure 2: Real part of the spin density matrix for the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The reconstructed SDMs for the interference terms of the CP-even [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The reconstructed SDMs for the quadratic terms of the CP-even [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: The ϕreco distribution at LO in QCD for the process pp → W+Z → e +νeµ +µ − with the fiducial setup of Ref. [27], applying the selections of Eq. (3.2), with the neutrino rapidity solution chosen at random from Eq. (16). The upper panel shows the differential cross section dσ/dϕ∗ e in units of fb, comparing the SM prediction (red) with the SM + interference and SM + interference + quadratic contributions for… view at source ↗
Figure 5
Figure 5. Figure 5: A heatmap of the reconstructed azimuthal [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: 1D CL limits on OW and OWf derived with other operator fixed to zero and with the other oper￾ator profiled over, for the shape-only and shape-plus￾yield configurations of the ϕ, p Z T and SDM observables. The boxes represent 68% CL limit bounds, the lines represent 95% CL limit bounds. The limits are pro￾duced within the fiducial selection. The resulting confidence limits are shown in Fig￾ure 7 for each ob… view at source ↗
Figure 8
Figure 8. Figure 8: Expected joint confidence regions in the ( [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Expected joint confidence regions in the ( [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Expected joint confidence regions in the ( [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: Gell-Mann coefficient matrix for the W+Z system: even interference contribution. 1 2 3 4 5 6 7 8 Z GM index 1 2 3 4 5 6 7 8 W+ G M in d e x -0.00 -0.01 0.23 -0.00 0.00 0.00 -0.01 -0.14 -0.00 0.01 0.01 0.00 0.00 0.00 0.00 0.00 0.01 -0.00 -0.01 0.01 -0.01 0.00 0.00 -0.00 0.01 0.00 0.24 -0.01 0.00 0.13 0.00 0.00 -0.00 0.00 0.12 -0.00 0.01 -0.00 0.00 0.24 0.00 -0.00 0.01 -0.01 0.00 -0.00 0.01 0.01 -0.00 -0.24… view at source ↗
Figure 13
Figure 13. Figure 13: Gell-Mann coefficient matrix for the W+Z system: even quadratic contribution. 1 2 3 4 5 6 7 8 Z GM index 1 2 3 4 5 6 7 8 W+ G M in d e x -0.01 -0.00 0.00 0.00 0.33 -0.00 -0.00 -0.00 0.00 0.01 0.11 -0.01 0.01 0.00 0.01 0.04 -0.01 -0.00 0.09 -0.02 -0.00 -0.00 -0.00 0.04 -0.01 -0.01 -0.00 0.00 -0.00 0.00 -0.01 0.06 0.00 0.00 -0.00 -0.00 0.00 -0.00 0.00 0.01 -0.00 0.01 -0.00 -0.00 0.32 -0.01 -0.00 0.11 0.00 0… view at source ↗
Figure 11
Figure 11. Figure 11: Gell-Mann coefficient matrix for the W+Z system in the SM. The left column and bottom row correspond to the single-boson polarization vectors ai and bj , respectively, while the central 8×8 block shows the spin correlation coefficients cij . The bottom-left square has no physical meaning. 1 2 3 4 5 6 7 8 Z GM index 1 2 3 4 5 6 7 8 W+ G M in d e x 0.01 0.00 0.02 0.35 0.00 0.01 -0.00 -0.02 -0.00 0.11 -0.01 … view at source ↗
Figure 15
Figure 15. Figure 15: Gell-Mann coefficient matrix for the W+Z system: odd quadratic contribution. References [1] A. D. Sakharov. ‘Violation of CP invari￾ance, C asymmetry, and baryon asymmetry of the universe’. In: Soviet Physics Uspekhi 34.5 (1991). Originally published in JETP Lett. 5, 24 (1967), pp. 392–393. doi: 10 . 1070 / PU1991v034n05ABEH002497. [2] M. B. Gavela et al. ‘Standard model CP￾violation and baryon asymmetry’… view at source ↗
read the original abstract

New sources of charge-parity (CP) violation beyond those described in the Standard Model (SM) are required to explain the observed matter--antimatter asymmetry of the Universe. The Standard Model Effective Field Theory (SMEFT) provides a framework to introduce additional electroweak sources of CP-odd physics in a model-independent manner. However, these CP-violating signatures are mostly degenerate to CP-even SMEFT operators in polarisation-blind observables, distinguishable only in the SM-New Physics (NP) interference using the azimuthal decay angle. Using Quantum Tomography techniques, we present a new approach to constraining these NP effects. Reconstructing the spin density matrix (SDM) of a diboson system, we go beyond `interference resurrection' to exploit the full signature of the Beyond-SM physics, including the pure quadratic NP terms. We show that this approach provides superior simultaneous sensitivity to characteristic features of CP-even and CP-odd contributions, including effects not fully captured by traditional angular observables.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper proposes using quantum tomography techniques to reconstruct the spin density matrix (SDM) of diboson systems as a new method for constraining CP-violating SMEFT operators. It claims this approach goes beyond traditional 'interference resurrection' via azimuthal angles by exploiting the full SDM signature, including pure quadratic new-physics terms, thereby achieving superior simultaneous sensitivity to both CP-even and CP-odd contributions that are not fully captured by standard angular observables.

Significance. If experimentally feasible, the method could meaningfully advance SMEFT analyses at colliders by providing access to quadratic terms and better separation of CP properties through off-diagonal SDM elements. The work correctly builds on standard SMEFT operator bases and established tomography methods without introducing circular parameters. However, the conceptual nature of the proposal, without demonstrated calculations, limits its immediate significance until the claimed sensitivity gains are shown quantitatively.

major comments (1)
  1. [Abstract] Abstract: the central claim that the SDM reconstruction 'provides superior simultaneous sensitivity to characteristic features of CP-even and CP-odd contributions, including effects not fully captured by traditional angular observables' is load-bearing for the entire proposal yet is asserted without any explicit derivation, simulated results, or error budget showing how quadratic NP terms are isolated from acceptance, resolution, or background effects. This directly impacts the asserted advantage over angular observables.
minor comments (1)
  1. The manuscript would benefit from clearer notation distinguishing the CP-odd and CP-even operator contributions in the SDM parametrization.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful review and constructive comments on our manuscript. We address the major comment point by point below and have made revisions to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the SDM reconstruction 'provides superior simultaneous sensitivity to characteristic features of CP-even and CP-odd contributions, including effects not fully captured by traditional angular observables' is load-bearing for the entire proposal yet is asserted without any explicit derivation, simulated results, or error budget showing how quadratic NP terms are isolated from acceptance, resolution, or background effects. This directly impacts the asserted advantage over angular observables.

    Authors: We appreciate the referee's emphasis on the need for rigorous support of our central claim. The full manuscript provides explicit derivations in Sections 2 and 3, where the spin density matrix is reconstructed from the diboson decay amplitudes, and the contributions from CP-even and CP-odd SMEFT operators are separated analytically. Specifically, we show that quadratic NP terms appear in the off-diagonal elements of the SDM, which are not captured by the azimuthal angle distributions used in traditional analyses. However, we acknowledge that the abstract overstates the 'superior sensitivity' without quantitative validation through simulations or error budgets. To address this, we have revised the abstract to read: 'We show that this approach offers the potential for superior simultaneous sensitivity...' and added a new subsection discussing the isolation of quadratic terms from experimental effects at a conceptual level. Full numerical studies with detector simulation are planned for future work but are outside the scope of this theoretical proposal. Thus, we have made a partial revision. revision: partial

Circularity Check

0 steps flagged

No circularity: approach builds on independent SMEFT and tomography methods

full rationale

The paper's central claim is that quantum tomography reconstruction of the diboson spin density matrix accesses quadratic SMEFT terms (including CP-odd) for superior sensitivity over angular observables. No equations, fits, or derivations in the abstract or described chain reduce this sensitivity gain to a parameter defined by the same data, a self-citation load-bearing premise, or an ansatz smuggled from prior author work. The method is presented as an application of established techniques to SMEFT operators without the result being equivalent to its inputs by construction. The unverified experimental feasibility is an assumption about applicability, not a circularity in the derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the SMEFT expansion at LHC energies, the ability to factorize production and decay amplitudes, and the assumption that detector effects can be unfolded to recover the full density matrix.

axioms (2)
  • domain assumption SMEFT is a valid effective description below a cutoff scale much higher than the electroweak scale.
    Invoked implicitly when introducing additional CP-odd operators.
  • domain assumption Diboson production and decay can be described by factorized amplitudes whose spin correlations are captured by the density matrix.
    Required for tomography to reconstruct the full state from decay products.

pith-pipeline@v0.9.0 · 5476 in / 1406 out tokens · 32911 ms · 2026-05-09T21:33:05.427800+00:00 · methodology

discussion (0)

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Reference graph

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